An exercise in kinematics Mechanics

Question

Clare is driving along a road in her car , with henry following 40 m behind his car, They are both travelling at a speed of 25 m.s-1. Clare spots a problem ahead and brakes to a halt with an acceleration of -5 m.s-2 , Henry takes 0.2 Seconds to react , then brakes, but his brakes are poor and only give an acceleration of -4m.s-1 , Investigate what hapens

Answer 1

Hi Nona!

 

So, to start, Clare and Henry are separated by 40 m.  I think the most important aspect we probably want to investigate here is whether Henry's car will collide with Clare's.

 

Most pertinent to this question is the displacement (or distance, since the travel is presumed to be in a straight line) for both Clare's braking and Henry's braking.  First, let's take a look at Clare's displacement while stopping.  As usual, with kinematic situations with constant acceleration, if we want to solve for one kinematic quantity, we have to know at least three others.  

 

For Clare's braking, we have:

 

to find:  d_C

know:  a_C (= -5 m/s²), v_oC (= 25 m/s), v_C (=0, comes to a stop)

 

We can then solve for d using:

 

v_C² = v_oC²+2a_Cd_c

 

0 = (25 m/s)² + 2(-5 m/s²)d_c

 

0 = 625 - 10d_C

 

d_C = 62.5 m

 

Now, let's look at Henry's braking.  First, Henry takes 0.2 s to even start braking.  Over this time, he travels at constant speed v = 25 m/s for 0.2 s.  During that time, therefore, he must cover 25*0.2 = 5 m.

 

Then Henry brakes, and we know the same quantities as we did for Clare, just with a different value for acceleration.  Thus, for Henry:

 

0 = (25 m/s)² + 2(-4 m/s²)d_H

 

d_H = 78.13 m

 

So, from the time Clare starts to brake, Clare travels 62.5 m to stop, and Henry travels 5 m + 78.13 m = 83.13 m.  So Henry travels 83.13 m - 62.5 m = 20.63 m more to stop than Clare does.  However, if they started with 40 m between them, they should still be clear, only about half as far apart, once they both stop.

 

Hope this helps!  If the problem wants more or different information, we can look at that, too.